What is the answer to 2log_{3}(t)+log_{t}(9)=5 ?

The answer to 2log_{3}(t)+log_{t}(9)=5 is t=9,t=sqrt(3)

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2log_{3}(t)+log_{t}(9)=5

2 lo g_{3} (t) + lo g_{t} (9) = 5

t = 9, t = 3

Solution steps

2 lo g_{3} (t) + lo g_{t} (9) = 5

Apply log rules

2 lo g_{3} (t) + \frac{2}{lo g _{3} ( t )} = 5

Rewrite the equation with

lo g_{3} (t) = u

2 u + \frac{2}{u} = 5

Solve

2 u + \frac{2}{u} = 5 : u = 2, u = \frac{1}{2}

u = 2, u = \frac{1}{2}

Substitute back

u = lo g_{3} (t),

solve for

t

Solve

lo g_{3} (t) = 2 : t = 9

Solve

lo g_{3} (t) = \frac{1}{2} : t = 3

t = 9, t = 3

Verify Solutions:

t = 9

True

, t = 3

True

The solutions are

t = 9, t = 3

ln (x) + ln^{2} (x) = 3

- 11 + \frac{12}{T} = - 4 ln (T)

lo g_{10} (75) = lo g_{10} (11 x)

lo g_{3} (x^{5}) = 5

ln ((x - 4)^{2}) = 3.219

What is the answer to 2log_{3}(t)+log_{t}(9)=5 ?
The answer to 2log_{3}(t)+log_{t}(9)=5 is t=9,t=sqrt(3)
Solve for t: 2log_{3}(t)+log_{t}(9)=5
The solution is t=9,t=sqrt(3)